The views of Kathry Griener have received prominence in two recent Media Reports:
An internal report by Kathryn Greiner was conducted on behalf of the NSW and ACT Catholic Bishops in 2016.
It was tabled during this week's Senate estimates hearings and has now been published online.
The report cites evidence that funding is being diverted to schools in more populated areas of NSW to the detriment of those in rural and remote dioceses.
The report notes that Catholic education over the past 40 years has been the beneficiary of bipartisan public policy "that has increased funding to presently unprecedented levels".
It refers to a "flawed governance model" within the Catholic system and calls for a new body to be set up to deliver Catholic education in NSW and the ACT, replacing 11 different authorities.
This new entity would look after the way funding is distributed to "ensure efficient, accessible and needs-based allocation of resources to all schools regardless of geographical location or current resource levels"
"Catholic schooling now operates in an environment that demands transparency and is asking hard questions about the use of funding from governments.
"Governments of all political persuasions have put education sectors on notice that they are looking to ensure that funding provided to school systems goes to where it is intended the school and its students."
Ms Greiner acknowledges her recommendations are likely to face resistance from some within the Catholic education system.
"I am aware that much of what appears in this report is likely to meet with objection for a number of reasons," she said.
The report also notes "profoundly different" views about academic performance across schools "a fact which must be of concern to the Bishops".
"All dioceses would assert that they provide a high standard of education," Ms Greiner said.
"However, I could not identify any common criteria that was broadly accepted and by which all dioceses could be compared and measured."
Gonski Review panel member Kathryn Greiner says it would be a "disaster" if the Senate voted down the Turnbull government's new school funding model, making her the second panellist in two days to throw their support behind the changes.
On Tuesday, former NSW and South Australian department of education boss Ken Boston said Parliament was on the "threshold of a new deal of historic national importance" and it would be a "tragedy" if the opportunity were allowed to pass.
Education Minister Simon Birmingham and Senate kingmaker Nick Xenophon seized upon Dr Boston's comments as evidence the current funding system needs to be overhauled.
Ms Greiner, who recently conducted an internal review of the NSW Catholic school system, told Fairfax Media: "I agree 100 per cent with what Ken said - it would be a disaster for Australian education if this doesn't pass.
"This is the first time a government in this country has drawn a line in the sand, removed the funding anomalies and got everybody on the same page."
She praised the government for cutting funding to private schools - including her alma mater, elite Sydney girls school Loreto Kirribilli - deemed significantly over-funded according to the needs-based formula.
"The Labor Party deserve credit for setting up the Gonski Review but they squibbed it when they said no school would lose any funding," she said.
"Gonski 2.0 delivers what the Gonski report wanted: an accountable, transparent, equitable, sector-blind funding formula."
Last year, Ms Greiner conducted a review of Catholic school governance and funding for the NSW and ACT bishops that questioned the practice of redistributing funding from poor dioceses to more popular schools.
She said the Catholic sector should end its campaign against the government and instead tackle the "enormous waste" in its administrative structures.
"It is a disgrace that this has been allowed to go on so long," she said of the 11 separate Catholic school authorities in NSW.
"A lot of money is being spent on administration that should go to children who need it.
"The Catholic sector has been on thin ice for a long time."
Ms Greiner served as a Liberal-aligned member of Sydney City Council for almost a decade and has sat on many company and non-profit boards.
Senator Birmingham said: "It's an indictment on [Opposition Leader] Bill Shorten to have the likes of Ken Boston out there saying this is fair, needs-based funding and the legislation should pass yet Labor continues to stand against it."
Senator Xenophon said: "I like to think that with some sensible compromises we can get this through because this is an increase in funding."